For over two millennia, Aristotle's logic has ruled over the thinking of western intellectuals. All precise theories, all scientific models, even models of the process of thinking itself, have in principle conformed to the straight-jacket of logic. But from its shady beginnings devising gambling strategies and counting corpses in medieval London, probability theory and statistical inference now emerge as better foundations for scientific models, especially those of the process of thinking and as essential ingredients of theoretical mathematics, even the foundations of mathematics itself. We propose that this see change in our perspective will affect virtually all of mathematics in the next century.
Referenze Bibliografiche
[1]
P. J. DAVIS -
R. HERSH,
The Mathematical Experience.
Birkhäuser Boston, Cambridge Mass.
1980. |
Zbl 0459.00001[2] WEINAN E. - K. KHANIN - A. MAZEL - YA SINAI, Probability distribution fonctions for the random forced Burger's equation. Phys. Rev. Letters, 78, 1997, 1904-1907.
[3]
C. FREILING,
Axioms of symmetry: throwing darts at the real line.
J. Symb. Logic,
51,
1986, 190-200. |
Zbl 0619.03035[4] N. GORDON - D. SALMOND - A. SMITH, Novel Approach to non-linear/non-Gaussian Bayesian State Estimation. IEEE Proc. F, 140, 1993, 107-113.
[5]
U. GRENANDER -
Y. CHOW -
D.M. KEENAN ,
HANDS: A Pattern Theoretic Study of Biological Shapes.
Springer-Verlag, New York
1991. |
Zbl 0808.68018[6] C. GROSS, Aristotle on the Brain. The Neuroscientist, 1, 1995, 245-250.
[7]
P. W. HALLINAN -
G. GORDON -
A. L. YUILLE -
P. GIBLIN -
D. MUMFORD,
Two and Three-dimensional Patterns of the Face.
AKPeters 1999. |
Zbl 0930.68140[8] M. ISARD - A. BLAKE, Contour tracking by stochastic propagation of conditional density. Proc. European Conference on Computer Vision. Vol. 1, Cambridge UK 1996, 343-356.
[9] E.T. JAYNES, Probability Theory: The Logic of Science. Available at http://bayes.wustl.edu/etj/prob.html. To be published by Camb. Univ. Press, 1996-2000.
[10] K. KANAZAWA - D. KOLLER - S. J. RUSSEL, Stochastic simulation algorithms for dynamic probabilistic networks. Proc. of the 11th Annual Conference on Uncertainty in AI (UAI). Montreal, Canada, August 1995,346-351.
[11]
S. LAURITZEN -
D. SPIEGELHALTER,
Local computations with probabilities on graphical structures.
J. Royal Stat. Soc., B
50,
1988, 157-224. |
Zbl 0684.68106[12] A. A. MUMFORD - M. YOUNG, The interrelationships of the physical measurements and the vital capacity. Biometrika, 15, 1923, 109-115.
[13]
J. PEARL,
Probabilistic Reasoning in Intelligent Systems.
Morgan Kaufman Publ., San Mateo, Calif.,
1988. |
Zbl 0746.68089[14] B. RUSSELL - A. N. WHITEHEAD, Principia Mathematica, vol. 2. Cambridge Univ. Press, 1912.
[15]
S. SHELAH -
W. H. WOODIN,
Large cardinals imply that every reasonable definable set is Lebesgue measurable.
Israel J. Math.,
70,
1990, 381-394. |
Zbl 0705.03028[16]
J. SPENCER,
Ten Lectures on the Probabilistic Method.
SIAM, 2nd ed., Philadelphia
1994. |
Zbl 0822.05060[17] B. WIDROW, The rubber mask technique. Pattern Recognition, 5, 1973, 175-211.
Con il contributo del Ministero per i Beni e le Attività Culturali